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PATTERNS
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Lets begin with Linear patterns. They are probably the easiest to recognize because the change is related to slope of a line.
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
EXAMPLE #1 : What pattern is shown in the graph ?
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
EXAMPLE #1 : What pattern is shown in the graph ?
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
EXAMPLE #1 : What pattern is shown in the graph ?
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
EXAMPLE #1 : What pattern is shown in the graph ?
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Geometric patterns can be represented numerically and generalized algebraically.
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Geometric patterns can be represented numerically and generalized algebraically.
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Let’s create a table to see the relationship between each build and the number of blocks…
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Let’s create a table to see the relationship between each build and the number of blocks…Build # Descriptio
nProcess # of
blocks
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Let’s create a table to see the relationship between each build and the number of blocks…Build # Descriptio
nProcess # of
blocks
1 1 row of 2 plus 1
1(2)+1 3
Build #1
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Let’s create a table to see the relationship between each build and the number of blocks…Build # Descriptio
nProcess # of
blocks
1 1 row of 2 plus 1
1(2)+1 3
2 2 rows of 2 plus 1 2(2)+1 5
Build #1
Build #2
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Let’s create a table to see the relationship between each build and the number of blocks…Build # Descriptio
nProcess # of
blocks
1 1 row of 2 plus 1
1(2)+1 3
2 2 rows of 2 plus 1 2(2)+1 5
3 3 rows of 2 plus 1 3(2)+1 7
Build #1
Build #2
Build #3
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Let’s create a table to see the relationship between each build and the number of blocks…Build # Descriptio
nProcess # of
blocks
1 1 row of 2 plus 1
1(2)+1 3
2 2 rows of 2 plus 1 2(2)+1 5
3 3 rows of 2 plus 1 3(2)+1 7
Build #1
Build #2
Build #3
The number changing in each build is the number of rows of two.
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Let’s create a table to see the relationship between each build and the number of blocks…Build # Descriptio
nProcess # of
blocks
1 1 row of 2 plus 1
1(2)+1 3
2 2 rows of 2 plus 1 2(2)+1 5
3 3 rows of 2 plus 1 3(2)+1 7
Build #1
Build #2
Build #3
PATTERNS
There are 4 types of patterns :1. Geometric2. Linear3. nth term4. Quadratic
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
1st Find the difference for each consecutive term
14 – (-1) = 15 39 – 14 = 25 74 – 39 = 35119 – 74 = 45
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Since the differences are NOT CONSTANT, we need to find the difference between the differences we just found…
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #3 : What is the tenth term of the pattern below ?
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #3 : What is the tenth term of the pattern below ?
The difference is constant, so a linear pattern.
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #3 : What is the tenth term of the pattern below ?
The difference is constant, so a linear pattern.
The pattern is decreasing so coefficient will be negative.
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #3 : What is the tenth term of the pattern below ?
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #3 : What is the tenth term of the pattern below ?
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #3 : What is the tenth term of the pattern below ?
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #4 : Write the first five terms of the pattern from the given expression below.
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #4 : Write the first five terms of the pattern from the given expression below.
Just start plugging in values for “n” starting with 1…
Nth term Patterns- look at the difference between the terms- if the differences are constant, the expression is linear- if the differences are not constant, look at the differences
between the differences- if the second differences are constant, then the expression
will be a quadratic expression
EXAMPLE #4 : Write the first five terms of the pattern from the given expression below.
Just start plugging in values for “n” starting with 1…
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
First differences are not constant…
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
EXAMPLE #5 : What function does the pattern below represent ?
